A model for the effect of pressure gradient on the induction and power of wind turbines

Recent studies have shown that streamwise variations in base flow velocity and the resulting pressure gradients can affect the induction and power of wind turbines. However, current research lacks analytical models that explicitly predict the effect of pressure gradient on the turbine induction and power. In this work, we extend the classical one-dimensional momentum theory to account for pressure gradients, using the Bernoulli equation, as well as mass and momentum conservation principles. In doing so, we develop analytical expressions for the induction and power of a turbine operating under a pressure gradient. To validate the model, we perform large-eddy simulations of a turbine positioned at the edge of a linear ramp, simulating a range of pressure gradients. The model is also compared with previously published wind tunnel experiments for the power predictions. The results show that the maximum error in predicting the induction factor is reduced by approximately a factor of four using the developed model compared to the classical approach. Similarly, the maximum error in predicting the power coefficient and power output is reduced by approximately a factor of two using the developed model compared to the classical approach. Overall, the model developed in this work improves upon the classical momentum theory by incorporating the influence of pressure gradients, enabling more accurate predictions of turbine power efficiency under such conditions.